And he has spoken of two key substitutions during the second half of the 1-1 draw with Everton.
Pascal Gross fired the Seagulls ahead after a clever dummy by sub Charalampos Koustoulas, who had replaced Danny Welbeck.
Gross was removed a minute from time with James Milner going on.
Everton levelled in the remaining seconds amid some chaotic Albion defending and a failure to keep possession.
The Seagulls have won just one of their last 11 league games.
Hurzeler said: “I think we showed another good performance.
“In the end, I said before the game, we have to manage the key moments better.
“And I think in one moment, we weren't alive, we didn't manage it well, and this cost us the game.
“We have to analyse it. I know that in the end in football, it's about results, but I think the key thing is that we are that we are there. We are close.
“We are getting where we want and just the key bits are the most important in football, that you really defend until the end of the game, that you manage the game well until the end of the game.
“We weren't able to do this in this game. So it feels painful, but we will overcome this phase and we will go again.”
Asked about substitutions, Hurzeler said: “I think Pascal was good in the game and therefore we wanted to have Pascal on the pitch.
“Of course, in the end, in additional time, we changed because we wanted to waste a little bit of time.”
Jack Hinshelwood was not an option to come off the bench due to illness.